The structure of molten NaCl is investigated by combining neutron and x-ray diffraction with molecular dynamics simulations that employed interaction potentials with either rigid or polarizable ions. Special attention is paid to the asymptotic decay of the pair-correlation functions, which is related to the small-k behavior of the partial structure factors, where k denotes the magnitude of the scattering vector. The rigid-ion approach gives access to an effective restricted primitive model in which the anion and cation have equal but opposite charges and are otherwise identical. For this model, the decay of the pair-correlation functions is in qualitative agreement with simple theory. The polarizable ion approach gives a good account of the diffraction results and yields thermodynamic parameters (density, isothermal compressibility, Debye screening length, and heat capacity) in accord with experiment. The longest decay length for the partial pair-distribution functions is a factor of ≃2.5 times greater than the nearest-neighbor distance. The results are commensurate with the decay lengths found for the effective restricted primitive model, which are much shorter than those found in experiments on concentrated electrolytes or ionic liquids using surface force apparatus.